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Modified from Stanford CS276 slides Chap. 13: Text Classification; The Naive Bayes algorithm

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## Modified from Stanford CS276 slides Chap. 13: Text Classification; The Naive Bayes algorithm

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Relevance feedback revisited

- In relevance feedback, the user marks a few documents as relevant/nonrelevant
- The choices can be viewed as classes or categories
- For several documents, the user decides which of these two classes is correct
- The IR system then uses these judgments to build a better model of the information need
- So, relevance feedback can be viewed as a form of text classification (deciding between several classes)
- The notion of classification is very general and has many applications within and beyond IR

Standing queries

- The path from IR to text classification:
- You have an information need to monitor, say:
- Unrest in the Niger delta region
- You want to rerun an appropriate query periodically to find new news items on this topic
- You will be sent new documents that are found
- I.e., it’s text classification not ranking
- Such queries are called standing queries
- Long used by “information professionals”
- A modern mass instantiation is Google Alerts
- Standing queries are (hand-written) text classifiers

Spam filtering: Another text classification task

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Text classification

- Today:
- Introduction to Text Classification
- Also widely known as “text categorization”. Same thing.
- Naïve Bayes text classification
- Including a little on Probabilistic Language Models

Categorization/Classification

- Given:
- A description of an instance, d X
- X is the instance language or instance space.
- Issue: how to represent text documents.
- Usually some type of high-dimensional space
- A fixed set of classes:

C ={c1, c2,…, cJ}

- Determine:
- The category of d: γ(d) C, where γ(d) is a classification function whose domain is X and whose range is C.
- We want to know how to build classification functions (“classifiers”).

Supervised Classification

- Given:
- A description of an instance, d X
- X is the instance language or instance space.
- A fixed set of classes:

C ={c1, c2,…, cJ}

- A training set D of labeled documents with each labeled document <d,c>∈X×C
- Determine:
- A learning method or algorithm which will enable us to learn a classifier γ:X→C
- For a test document d, we assign it the class γ(d) ∈ C

Document Classification

“planning

language

proof

intelligence”

Test

Data:

(AI)

(Programming)

(HCI)

Classes:

Planning

Semantics

Garb.Coll.

Multimedia

GUI

ML

Training

Data:

learning

intelligence

algorithm

reinforcement

network...

planning

temporal

reasoning

plan

language...

programming

semantics

language

proof...

garbage

collection

memory

optimization

region...

...

...

(Note: in real life there is often a hierarchy, not present in the above problem statement; and also, you get papers on ML approaches to Garb. Coll.)

More Text Classification ExamplesMany search engine functionalities use classification

- Assigning labels to documents or web-pages:
- Labels are most often topics such as Yahoo-categories
- "finance," "sports," "news>world>asia>business"
- Labels may be genres
- "editorials" "movie-reviews" "news”
- Labels may be opinion on a person/product
- “like”, “hate”, “neutral”
- Labels may be domain-specific
- "interesting-to-me" : "not-interesting-to-me”
- “contains adult language” : “doesn’t”
- language identification: English, French, Chinese, …
- search vertical: about Linux versus not
- “link spam” : “not link spam”

Classification Methods (1)

- Manual classification
- Used by the original Yahoo! Directory
- Looksmart, about.com, ODP, PubMed
- Very accurate when job is done by experts
- Consistent when the problem size and team is small
- Difficult and expensive to scale
- Means we need automatic classification methods for big problems

Classification Methods (2)

- Automatic document classification
- Hand-coded rule-based systems
- One technique used by CS dept’s spam filter, Reuters, CIA, etc.
- It’s what Google Alerts is doing
- Widely deployed in government and enterprise
- Companies provide “IDE” for writing such rules
- E.g., assign category if document contains a given boolean combination of words
- Standing queries: Commercial systems have complex query languages (everything in IR query languages +score accumulators)
- Accuracy is often very high if a rule has been carefully refined over time by a subject expert
- Building and maintaining these rules is expensive

A Verity topic A complex classification rule

- Note:
- maintenance issues (author, etc.)
- Hand-weighting of terms

[Verity was bought by Autonomy.]

Classification Methods (3)

- Supervised learning of a document-label assignment function
- Many systems partly rely on machine learning (Autonomy, Microsoft, Enkata, Yahoo!, …)
- k-Nearest Neighbors (simple, powerful)
- Naive Bayes (simple, common method)
- Support-vector machines (new, more powerful)
- … plus many other methods
- No free lunch: requires hand-classified training data
- But data can be built up (and refined) by amateurs
- Many commercial systems use a mixture of methods

Probabilistic relevance feedback

- Rather than reweighting in a vector space…
- If user has told us some relevant and some irrelevant documents, then we can proceed to build a probabilistic classifier,
- such as the Naive Bayes model we will look at today:
- P(tk|R) = |Drk| / |Dr|
- P(tk|NR) = |Dnrk| / |Dnr|
- tk is a term; Dr is the set of known relevant documents; Drk is the subset that contain tk; Dnr is the set of known irrelevant documents; Dnrk is the subset that contain tk.

Bayesian Methods

- Our focus this lecture
- Learning and classification methods based on probability theory.
- Bayes theorem plays a critical role in probabilistic learning and classification.
- Builds a generative model that approximates how data is produced
- Uses prior probability of each category given no information about an item.
- Categorization produces a posterior probability distribution over the possible categories given a description of an item.

Naive Bayes Classifiers

Task: Classify a new instance d based on a tuple of attribute values into one of the classes cj C

MAP is “maximum a posteriori” = most likely class

Naïve Bayes Classifier: Naïve Bayes Assumption

- P(cj)
- Can be estimated from the frequency of classes in the training examples.
- P(x1,x2,…,xn|cj)
- O(|X|n•|C|) parameters
- Could only be estimated if a very, very large number of training examples was available.

Naïve Bayes Conditional Independence Assumption:

- Assume that the probability of observing the conjunction of attributes is equal to the product of the individual probabilities P(xi|cj).

Flu

X1

X2

X3

X4

X5

runnynose

sinus

cough

fever

muscle-ache

The Naïve Bayes Classifier- Conditional Independence Assumption: features detect term presence and are independent of each other given the class:
- This model is appropriate for binary variables
- Multivariate Bernoulli model

C

X1

X2

X3

X4

X5

X6

Learning the Model- First attempt: maximum likelihood estimates
- simply use the frequencies in the data

What if we have seen no training documents with the word muscle-ache and classified in the topic Flu?

Zero probabilities cannot be conditioned away, no matter the other evidence!

Flu

X1

X2

X3

X4

X5

runnynose

sinus

cough

fever

muscle-ache

Problem with Maximum LikelihoodSomewhat more subtle version

Smoothing to Avoid Overfitting# of values ofXi

overall fraction in data where Xi=xi,k

extent of

“smoothing”

multiply

Stochastic Language Models- Model probability of generating strings (each word in turn) in a language (commonly all strings over alphabet ∑). E.g., a unigram model

Model M

0.2 the

0.1 a

0.01 man

0.01 woman

0.03 said

0.02 likes

…

the

man

likes

the

woman

0.2

0.01

0.02

0.2

0.01

P(s | M) = 0.00000008

the

class

pleaseth

yon

maiden

0.2

0.01

0.0001

0.0001

0.0005

0.2

0.0001

0.02

0.1

0.01

Stochastic Language Models- Model probability of generating any string

Model M1

Model M2

0.2 the

0.0001 class

0.03 sayst

0.02 pleaseth

0.1 yon

0.01 maiden

0.0001 woman

0.2 the

0.01 class

0.0001 sayst

0.0001 pleaseth

0.0001 yon

0.0005 maiden

0.01 woman

P(s|M2) > P(s|M1)

P ( ) P ( ) P ( ) P ( )

P ( )

P ( ) P ( | ) P ( | ) P ( | )

P ( | )

= P ( )

P ( | )

P ( | )

Unigram and higher-order models- Unigram Language Models
- Bigram (generally, n-gram) Language Models
- Other Language Models
- Grammar-based models (PCFGs), etc.
- Probably not the first thing to try in IR

Easy.

Effective!

Naïve Bayes via a class conditional language model = multinomial NB

- Effectively, the probability of each class is done as a class-specific unigram language model

C

w1

w2

w3

w4

w5

w6

Using Multinomial Naive Bayes Classifiers to Classify Text: Basic method

- Attributes are text positions, values are words.

- Still too many possibilities
- Assume that classification is independent of the positions of the words
- Use same parameters for each position
- Result is bag of words model (over tokens not types)

Naive Bayes: Learning

- From training corpus, extract Vocabulary
- Calculate required P(cj)and P(xk | cj)terms
- For each cj in Cdo
- docsjsubset of documents for which the target class is cj

- Textj single document containing all docsj
- for each word xkin Vocabulary
- nk number of occurrences ofxkin Textj

Naive Bayes: Classifying

- positions all word positions in current document which contain tokens found in Vocabulary
- Return cNB, where

Naive Bayes: Time Complexity

- Training Time: O(|D|Lave + |C||V|)) where Lave is the average length of a document in D.
- Assumes all counts arepre-computed in O(|D|Lave) time during one pass through all of the data.
- Generally just O(|D|Lave) since usually |C||V| < |D|Lave
- Test Time: O(|C| Lt) where Lt is the average length of a test document.
- Very efficient overall, linearly proportional to the time needed to just read in all the data.

Why?

Underflow Prevention: using logs

- Multiplying lots of probabilities, which are between 0 and 1 by definition, can result in floating-point underflow.
- Since log(xy) = log(x) + log(y), it is better to perform all computations by summing logs of probabilities rather than multiplying probabilities.
- Class with highest final un-normalized log probability score is still the most probable.
- Note that model is now just max of sum of weights…

Naive Bayes Classifier

- Simple interpretation: Each conditional parameter log P(xi|cj) is a weight that indicates how good an indicator xi is for cj.
- The prior log P(cj) is a weight that indicates the relative frequency of cj.
- The sum is then a measure of how much evidence there is for the document being in the class.
- We select the class with the most evidence for it

Two Naive Bayes Models

- Model 1: Multivariate Bernoulli
- One feature Xw for each word in dictionary
- Xw = true in document d if w appears in d
- Naive Bayes assumption:
- Given the document’s topic, appearance of one word in the document tells us nothing about chances that another word appears
- This is the model used in the binary independence model in classic probabilistic relevance feedback on hand-classified data (Maron in IR was a very early user of NB)

Two Models

- Model 2: Multinomial = Class conditional unigram
- One feature Xi for each word pos in document
- feature’s values are all words in dictionary
- Value of Xi is the word in position i
- Naïve Bayes assumption:
- Given the document’s topic, word in one position in the document tells us nothing about words in other positions
- Second assumption:
- Word appearance does not depend on position
- Just have one multinomial feature predicting all words

for all positions i,j, word w, and class c

Parameter estimation

- Multivariate Bernoulli model:
- Multinomial model:
- Can create a mega-document for topic j by concatenating all documents in this topic
- Use frequency of w in mega-document

fraction of documents of topic cj

in which word w appears

fraction of times in which

word w appears among all

words in documents of topic cj

Classification

- Multinomial vs Multivariate Bernoulli?
- Multinomial model is almost always more effective in text applications!
- See results figures later
- See IIR sections 13.2 and 13.3 for worked examples with each model

Feature Selection: Why?

- Text collections have a large number of features
- 10,000 – 1,000,000 unique words … and more
- May make using a particular classifier feasible
- Some classifiers can’t deal with 100,000 of features
- Reduces training time
- Training time for some methods is quadratic or worse in the number of features
- Can improve generalization (performance)
- Eliminates noise features
- Avoids overfitting

Feature selection: how?

- Two ideas:
- Hypothesis testing statistics:
- Are we confident that the value of one categorical variable is associated with the value of another
- Chi-square test (2)
- Information theory:
- How much information does the value of one categorical variable give you about the value of another
- Mutual information
- They’re similar, but 2 measures confidence in association, (based on available statistics), while MI measures extent of association (assuming perfect knowledge of probabilities)

Term = jaguar

Term jaguar

Class = auto

2

(0.25)

500

(502)

Class auto

3

(4.75)

9500

(9498)

2 statistic (CHI)- 2 is interested in (fo – fe)2/fe summed over all table entries: is the observed number what you’d expect given the marginals?
- The null hypothesis is rejected with confidence .999,
- since 12.9 > 10.83 (the value for .999 confidence).

expected: fe

observed: fo

A = #(t,c)

C = #(¬t,c)

B = #(t,¬c)

D = #(¬t, ¬c)

2 statistic (CHI)

There is a simpler formula for 2x2 2:

N = A + B + C + D

Value for complete independence of term and category?

Feature selection via Mutual Information

- In training set, choose k words which best discriminate (give most info on) the categories.
- The Mutual Information between a word, class is:
- For each word w and each category c

Feature selection via MI (contd.)

- For each category we build a list of k most discriminating terms.
- For example (on 20 Newsgroups):
- sci.electronics: circuit, voltage, amp, ground, copy, battery, electronics, cooling, …
- rec.autos: car, cars, engine, ford, dealer, mustang, oil, collision, autos, tires, toyota, …
- Greedy: does not account for correlations between terms
- Why?

Feature Selection

- Mutual Information
- Clear information-theoretic interpretation
- May select rare uninformative terms
- Chi-square
- Statistical foundation
- May select very slightly informative frequent terms that are not very useful for classification
- Just use the commonest terms?
- No particular foundation
- In practice, this is often 90% as good

Feature selection for NB

- In general feature selection is necessary for multivariate Bernoulli NB.
- Otherwise you suffer from noise, multi-counting
- “Feature selection” really means something different for multinomial NB. It means dictionary truncation
- The multinomial NB model only has 1 feature
- This “feature selection” normally isn’t needed for multinomial NB, but may help a fraction with quantities that are badly estimated

Evaluating Categorization

- Evaluation must be done on test data that are independent of the training data (usually a disjoint set of instances).
- Sometimes use cross-validation (averaging results over multiple training and test splits of the overall data)
- It’s easy to get good performance on a test set that was available to the learner during training (e.g., just memorize the test set).
- Measures: precision, recall, F1, classification accuracy
- Classification accuracy: c/n where n is the total number of test instances and c is the number of test instances correctly classified by the system.
- Adequate if one class per document
- Otherwise F measure for each class

WebKB Experiment (1998)

- Classify webpages from CS departments into:
- student, faculty, course,project
- Train on ~5,000 hand-labeled web pages
- Cornell, Washington, U.Texas, Wisconsin
- Crawl and classify a new site (CMU)
- Results:

SpamAssassin

- Naïve Bayes has found a home in spam filtering
- Paul Graham’s A Plan for Spam
- A mutant with more mutant offspring...
- Naive Bayes-like classifier with weird parameter estimation
- Widely used in spam filters
- Classic Naive Bayes superior when appropriately used
- According to David D. Lewis
- But also many other things: black hole lists, etc.
- Many email topic filters also use NB classifiers

Violation of NB Assumptions

- The independence assumptions do not really hold of documents written in natural language.
- Conditional independence
- Positional independence
- Examples?

Example: Sensors

NB FACTORS:

- P(s) = 1/2
- P(+|s) = 1/4
- P(+|r) = 3/4

Reality

Raining

Sunny

P(+,+,r) = 3/8

P(-,-,r) = 1/8

P(+,+,s) = 1/8

P(-,-,s) = 3/8

NB Model

PREDICTIONS:

- P(r,+,+) = (½)(¾)(¾)
- P(s,+,+) = (½)(¼)(¼)
- P(r|+,+) = 9/10
- P(s|+,+) = 1/10

Raining?

M1

M2

Naïve Bayes Posterior Probabilities

- Classification results of naïve Bayes (the class with maximum posterior probability) are usually fairly accurate.
- However, due to the inadequacy of the conditional independence assumption, the actual posterior-probability numerical estimates are not.
- Output probabilities are commonly very close to 0 or 1.
- Correct estimation accurate prediction, but correct probability estimation is NOT necessary for accurate prediction (just need right ordering of probabilities)

Naive Bayes is Not So Naive

- Naive Bayes won 1st and 2nd place in KDD-CUP 97 competition out of 16 systems

Goal: Financial services industry direct mail response prediction model: Predict if the recipient of mail will actually respond to the advertisement – 750,000 records.

- More robust to irrelevant features than many learning methods

Irrelevant Features cancel each other without affecting results

Decision Trees can suffer heavily from this.

- More robust to concept drift (changing class definition over time)
- Very good in domains with many equally important features

Decision Trees suffer from fragmentation in such cases – especially if little data

- A good dependable baseline for text classification (but not the best)!
- Optimal if the Independence Assumptions hold: Bayes Optimal Classifier

Never true for text, but possible in some domains

- Very Fast Learning and Testing (basically just count the data)
- Low Storage requirements

Resources for today’s lecture

- IIR 13
- Fabrizio Sebastiani. Machine Learning in Automated Text Categorization. ACM Computing Surveys, 34(1):1-47, 2002.
- Yiming Yang & Xin Liu, A re-examination of text categorization methods. Proceedings of SIGIR, 1999.
- Andrew McCallum and Kamal Nigam. A Comparison of Event Models for Naive Bayes Text Classification. In AAAI/ICML-98 Workshop on Learning for Text Categorization, pp. 41-48.
- Tom Mitchell, Machine Learning. McGraw-Hill, 1997.
- Clear simple explanation of Naïve Bayes
- Open Calais: Automatic Semantic Tagging
- Free (but they can keep your data), provided by Thompson/Reuters (ex-ClearForest)
- Weka: A data mining software package that includes an implementation of Naive Bayes
- Reuters-21578 – the most famous text classification evaluation set
- Still widely used by lazy people (but now it’s too small for realistic experiments – you should use Reuters RCV1)

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